{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/master/latent_variable_models_part_1.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    # Check if notebook is running in Google Colab\n",
    "    import google.colab\n",
    "    # Get additional files from Github\n",
    "    !wget https://raw.githubusercontent.com/krasserm/bayesian-machine-learning/master/latent_variable_models_util.py\n",
    "    # Install additional dependencies\n",
    "    !pip install daft==0.1.0\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Latent variable models, part 1: Gaussian mixture models and the EM algorithm\n",
    "\n",
    "This is part 1 of a two-part series of articles about latent variable models. Part 1 covers the expectation maximization (EM) algorithm and its application to Gaussian mixture models. [Part 2](latent_variable_models_part_2.ipynb) covers approximate inference and variational autoencoders.\n",
    "\n",
    "## Introduction\n",
    "\n",
    "Given a probabilistic model $p(\\mathbf{x} \\lvert \\boldsymbol{\\theta})$ and $N$ observations $\\mathbf{X} = \\left\\{ \\mathbf{x}_1, \\ldots, \\mathbf{x}_N \\right\\}$ we often want to find a value for parameter $\\boldsymbol{\\theta}$ that maximizes the likelihood function $p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$, a function of parameter $\\boldsymbol{\\theta}$. This is known as [maximimum likelihood estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) (MLE). \n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\theta}_{MLE} = \\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})\n",
    "\\tag{1}\n",
    "$$\n",
    "\n",
    "If the model is a simple probability distribution, like a single Gaussian, for example, then $\\boldsymbol{\\theta}_{MLE} = \\left\\{ \\boldsymbol{\\mu}_{MLE}, \\boldsymbol{\\Sigma}_{MLE} \\right\\}$ has an analytical solution. A common approach for more complex models is *gradient descent* using the *negative log likelihood*, $-\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$, as loss function. This can easily be implemented with frameworks like PyTorch or Tensorflow provided that $p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$ is differentiable w.r.t. $\\boldsymbol{\\theta}$. But this is not necessarily the most efficient approach.\n",
    "\n",
    "## Gaussian mixture model\n",
    "\n",
    "MLE can often be simplified by introducing *latent variables*. A latent variable model makes the assumption that an observation $\\mathbf{x}_i$ is caused by some underlying latent variable, a variable that cannot be observed directly but can be inferred from observed variables and parameters. For example, the following plot shows observations in 2-dimensional space and one can see that their overall distribution doesn't seem follow a simple distribution like a single Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from latent_variable_models_util import n_true, mu_true, sigma_true\n",
    "from latent_variable_models_util import generate_data, plot_data, plot_densities\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "X, T = generate_data(n=n_true, mu=mu_true, sigma=sigma_true)\n",
    "\n",
    "plot_data(X, color='grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we can see that there are clusters of higher density. Also, the distribution within a cluster looks more like a Gaussian compared to the overall distribution. Indeed, these data were generated using a *mixture* of three Gaussians as shown in the following plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(X, color=T)\n",
    "plot_densities(X, mu=mu_true, sigma=sigma_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The underlying probabilistic model is called a *Gaussian mixture model* (GMM), a weighted sum of $C$ Gaussian components where $C=3$ in this example.\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x} \\lvert \\boldsymbol{\\theta}) = \\sum_{c=1}^{C} \\pi_c \\mathcal{N}(\\mathbf{x} \\lvert \\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)\n",
    "\\tag{2}\n",
    "$$\n",
    "\n",
    "$\\pi_c$, $\\boldsymbol{\\mu}_{c}$ and $\\boldsymbol{\\Sigma}_{c}$ are the weight, mean vector and covariance matrix of mixture component $c$, respectively. The weights are non-negative and sum up to $1$ i.e. $\\sum_{c=1}^{C} \\pi_c = 1$. Parameter vector $\\boldsymbol{\\theta} = \\left\\{ \\pi_1, \\boldsymbol{\\mu}_{1}, \\boldsymbol{\\Sigma}_{1}, \\ldots, \\pi_C, \\boldsymbol{\\mu}_{C}, \\boldsymbol{\\Sigma}_{C} \\right\\}$ denotes the set of all model parameters. If we introduce a discrete latent variable $\\mathbf{t}$ that determines the assignment of observations to mixture components we can define a joint distribution over observed and latent variables $p(\\mathbf{x}, \\mathbf{t} \\lvert \\boldsymbol{\\theta})$ in terms of a conditional distribution $p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta})$ and a prior distribution $p(\\mathbf{t} \\lvert \\boldsymbol{\\theta})$\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}, \\mathbf{t} \\lvert \\boldsymbol{\\theta}) = p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta}) p(\\mathbf{t} \\lvert \\boldsymbol{\\theta})\n",
    "\\tag{3}\n",
    "$$\n",
    "\n",
    "where $p(\\mathbf{x} \\lvert t_c = 1, \\boldsymbol{\\theta}) = \\mathcal{N}(\\mathbf{x} \\lvert \\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)$ and $p(t_c = 1 \\lvert \\boldsymbol{\\theta}) = \\pi_c$. The values of $\\mathbf{t}$ are one-hot encoded. For example, $t_2 = 1$ refers to the second mixture component  which means $\\mathbf{t} = (0,1,0)^T$ if there are $C=3$ components in total. The marginal distribution $p(\\mathbf{x} \\lvert \\boldsymbol{\\theta})$ is obtained by summing over all possible states of $\\mathbf{t}$.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(\\mathbf{x} \\lvert \\boldsymbol{\\theta}) &= \n",
    "\\sum_{c=1}^{C} p(t_c = 1 \\lvert \\boldsymbol{\\theta}) p(\\mathbf{x} \\lvert t_c = 1, \\boldsymbol{\\theta}) \\\\ &= \n",
    "\\sum_{c=1}^{C} \\pi_c \\mathcal{N}(\\mathbf{x} \\lvert \\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)\n",
    "\\tag{4}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "For each observation $\\mathbf{x}_i$ we have one latent variable $\\mathbf{t}_i$, as shown in the following plate notation of the model.\n",
    "\n",
    "![gmm](images/gmm/gmm.png)\n",
    "\n",
    "We denote the set of all observations by $\\mathbf{X}$ and the set of all latent variables by $\\mathbf{T}$. If we could observe $\\mathbf{T}$ directly, we could easily maximize the *complete-data likelihood* $p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})$ because we would then know the assignment of data points to components, and fitting a single Gaussian per component can be done analytically. But since we can only observe $\\mathbf{X}$, we have to maximize the *marginal likelihood* or *incomplete-data likelihood* $p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$. By using the logarithm of the likelihood we have \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\boldsymbol{\\theta}_{MLE} &= \n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) \\\\ &=\n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\log \\sum_{T} p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})\n",
    "\\tag{5}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "which involves a summation over latent variables inside the logarithm. This prevents a simple analytical solution to the optimization problem. \n",
    "\n",
    "## Expectation maximization algorithm\n",
    "\n",
    "Although we cannot observe latent variables directly, we can obtain their posterior distribution. We start with a preliminary parameter value $\\boldsymbol{\\theta}^{old}$.\n",
    "\n",
    "$$\n",
    "p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}^{old}) = {\n",
    "{p(\\mathbf{X} \\lvert \\mathbf{T}, \\boldsymbol{\\theta}^{old}) p(\\mathbf{T} \\lvert \\boldsymbol{\\theta}^{old})} \\over \n",
    "{\\sum_{T} p(\\mathbf{X} \\lvert \\mathbf{T}, \\boldsymbol{\\theta}^{old}) p(\\mathbf{T} \\lvert \\boldsymbol{\\theta}^{old})}}\n",
    "\\tag{6}\n",
    "$$\n",
    "\n",
    "This allows us to define an *<ins>e</ins>xpectation* of the complete-data likelihood w.r.t. to the posterior distribution. \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mathcal{Q}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{old}) &= \n",
    "\\sum_{T} p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}^{old}) \\log p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta}) \\\\ &= \n",
    "\\mathbb{E}_{p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}^{old})} \\log p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})\n",
    "\\tag{7}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This expectation is then *<ins>m</ins>aximized* w.r.t. to $\\boldsymbol{\\theta}$ resulting in an updated parameter vector $\\boldsymbol{\\theta}^{new}$.\n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\theta}^{new} = \\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\mathcal{Q}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{old})\n",
    "\\tag{8}\n",
    "$$\n",
    "\n",
    "In Eq. $(7)$ the summation is outside the logarithm which enables an analytical solution for $\\boldsymbol{\\theta}^{new}$ in the case of GMMs. We then let $\\boldsymbol{\\theta}^{old} \\leftarrow \\boldsymbol{\\theta}^{new}$ and repeat these steps until convergence. This is the essence of the *expectation maximization (EM) algorithm*. It has an expectation- or *E-step* where the posterior over latent variables is obtained and a maximization- or *M-step* where the expectation of the complete-data likelihood w.r.t. the posterior distribution is maximized. It can be shown that the EM algorithm always converges to a local maximum of $p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$. The following subsection describes the EM algorithm in a more general form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### General form\n",
    "\n",
    "By introducing a latent variable $\\mathbf{t}_i$ for each observation $\\mathbf{x}_i$ we can define the log marginal likelihood as\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) &=\n",
    "\\sum_{i=1}^{N} \\log p(\\mathbf{x}_i \\lvert \\boldsymbol{\\theta}) \\\\ &=\n",
    "\\sum_{i=1}^{N} \\log \\sum_{c=1}^{C} p(\\mathbf{x}_i, t_{ic} = 1 \\lvert \\boldsymbol{\\theta})\n",
    "\\tag{9}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Next we introduce a distribution $q(\\mathbf{t}_i)$ over latent variable $\\mathbf{t}_i$, which can be any probability distribution, and multiply and divide the RHS of the Eq. $(9)$ with this distribution.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) &=\n",
    "\\sum_{i=1}^{N} \\log \\sum_{c=1}^{C} q(t_{ic} = 1) {{p(\\mathbf{x}_i, t_{ic} = 1 \\lvert \\boldsymbol{\\theta})} \\over {q(t_{ic} = 1)}} \\\\ &= \n",
    "\\sum_{i=1}^{N} \\log \\mathbb{E}_{q(\\mathbf{t}_i)} {{p(\\mathbf{x}_i, \\mathbf{t}_i \\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i)}}\n",
    "\\tag{10}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "We now have a concave function ($\\log$) of an expectation which allows us to apply [Jensen's inequality](https://en.wikipedia.org/wiki/Jensen%27s_inequality) to define a *lower bound* $\\mathcal{L}$ on $\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$. \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) &=\n",
    "\\sum_{i=1}^{N} \\log \\mathbb{E}_{q(\\mathbf{t}_i)} {{p(\\mathbf{x}_i, \\mathbf{t}_i\\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i)}} \\\\ &\\geq\n",
    "\\sum_{i=1}^{N} \\mathbb{E}_{q(\\mathbf{t}_i)} \\log {{p(\\mathbf{x}_i, \\mathbf{t}_i\\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i)}} \\\\ &=\n",
    "\\mathbb{E}_{q(\\mathbf{T})} \\log {{p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{T})}} \\\\ &=\n",
    "\\mathcal{L}(\\boldsymbol{\\theta}, q)\n",
    "\\tag{11}\n",
    "\\end{align*} \n",
    "$$\n",
    "\n",
    "This lower bound is a function of $\\boldsymbol{\\theta}$ and $q$. When we subtract the lower bound from the log marginal likelihood we should end up with something that is non-negative.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) - \\mathcal{L}(\\boldsymbol{\\theta}, q) &= \n",
    "\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) - \\mathbb{E}_{q(\\mathbf{T})} \\log {{p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{T})}} \\\\ &=\n",
    "\\mathbb{E}_{q(\\mathbf{T})} \\log {{p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) q(\\mathbf{T})} \\over {p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})}} \\\\ &=\n",
    "\\mathbb{E}_{q(\\mathbf{T})} \\log {{q(\\mathbf{T})} \\over {p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta})}} \\\\ &=\n",
    "\\mathrm{KL}(q(\\mathbf{T}) \\mid\\mid p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}))\n",
    "\\tag{12}\n",
    "\\end{align*}\n",
    "$$\n",
    "                                 \n",
    "We end up with the Kullback-Leibler (KL) divergence between $q(\\mathbf{T})$ and the true posterior over latent variables. It can be shown that the KL divergence is always non-negative. We finally can write the following expression for the lower bound.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(\\boldsymbol{\\theta}, q) = \\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) - \\mathrm{KL}(q(\\mathbf{T}) \\mid\\mid p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}))\n",
    "\\tag{13}\n",
    "$$\n",
    "\n",
    "In the E-step of the EM algorithm $\\mathcal{L}(\\boldsymbol{\\theta}, q)$ is maximized w.r.t. $q$ and $\\boldsymbol{\\theta}$ is held fixed.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "q^{new} &= \n",
    "\\underset{q}{\\mathrm{argmax}} \\mathcal{L}(\\boldsymbol{\\theta}^{old}, q) \\\\ &=\n",
    "\\underset{q}{\\mathrm{argmin}} \\mathrm{KL}(q(\\mathbf{T}) \\mid\\mid p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}^{old}))\n",
    "\\tag{14}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "\n",
    "$\\mathcal{L}(\\boldsymbol{\\theta}, q)$ is maximized when $\\mathrm{KL}(q(\\mathbf{T}) \\mid\\mid p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}))$ is minimized as $\\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$ doesn't depend on $q$. If we can obtain the true posterior, like in the GMM case, we can set $q(\\mathbf{T})$ to $p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta})$ and the KL divergence becomes $0$. If the true posterior is not tractable we have to use approximations. One family of approximation techniques is called *variational inference* which uses specific forms of $q$ to approximate the true posterior. For example, $q$ may come from a parameteric family of distributions and the parameters of $q$ are chosen such that the KL divergence is minimized. Variational inference is covered in more detail in part 2.\n",
    "\n",
    "In the M-step $\\mathcal{L}(\\boldsymbol{\\theta}, q)$ is maximized w.r.t. $\\boldsymbol{\\theta}$ and $q$ is held fixed.  Using Eq. $(11)$ we get\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\boldsymbol{\\theta}^{new} &= \n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\mathcal{L}(\\boldsymbol{\\theta}, q^{new}) \\\\ &=\n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\mathbb{E}_{q^{new}(\\mathbf{T})} \\log {{p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta})} \\over {q^{new}(\\mathbf{T})}} \\\\ &=\n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\mathbb{E}_{q^{new}(\\mathbf{T})} \\log p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta}) - \\mathbb{E}_{q^{new}(\\mathbf{T})} \\log q^{new}(\\mathbf{T}) \\\\ &=\n",
    "\\underset{\\boldsymbol{\\theta}}{\\mathrm{argmax}} \\mathbb{E}_{q^{new}(\\mathbf{T})} \\log p(\\mathbf{X}, \\mathbf{T} \\lvert \\boldsymbol{\\theta}) +\\mathrm{const.}\n",
    "\\tag{15}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "If the true posterior is known Eq. $(15)$ becomes Eq. $(7)$ except for the constant term which can be ignored during optimization. Again, we let $\\boldsymbol{\\theta}^{old} \\leftarrow \\boldsymbol{\\theta}^{new}$ and repeat these steps until convergence. The next section applies the EM algorithm to GMMs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expectation maximization algorithm for GMMs\n",
    "\n",
    "The parameters for a GMM with 3 components are $\\boldsymbol{\\theta} = \\left\\{ \\pi_1, \\boldsymbol{\\mu}_{1}, \\boldsymbol{\\Sigma}_{1}, \\pi_2, \\boldsymbol{\\mu}_{2}, \\boldsymbol{\\Sigma}_{2}, \\pi_3, \\boldsymbol{\\mu}_{3}, \\boldsymbol{\\Sigma}_{3} \\right\\}$. The prior probability for component $c$ is $p(t_c = 1 \\lvert \\boldsymbol{\\theta}) = \\pi_c$ and the conditional distribution of $\\mathbf{x}$ given the latent variable value for this component is $p(\\mathbf{x} \\lvert t_c = 1, \\boldsymbol{\\theta}) = \\mathcal{N}(\\mathbf{x} \\lvert \\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)$.\n",
    "\n",
    "### Implementation with numpy and scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from scipy.stats import multivariate_normal as mvn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the E-step we set $q(\\mathbf{T})$ to the known posterior $ p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta})$ using Eq. $(6)$ and compute the posterior probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def e_step(X, pi, mu, sigma):\n",
    "    \"\"\"\n",
    "    Computes posterior probabilities from data and parameters.\n",
    "    \n",
    "    Args:\n",
    "        X: observed data (N, D).\n",
    "        pi: prior probabilities (C,).\n",
    "        mu: mixture component means (C, D).\n",
    "        sigma: mixture component covariances (C, D, D).\n",
    "\n",
    "    Returns:\n",
    "        Posterior probabilities (N, C).\n",
    "    \"\"\"\n",
    "\n",
    "    N = X.shape[0]\n",
    "    C = mu.shape[0]\n",
    "    q = np.zeros((N, C))\n",
    "\n",
    "    # Equation (6)\n",
    "    for c in range(C):\n",
    "        q[:, c] = mvn(mu[c], sigma[c]).pdf(X) * pi[c]        \n",
    "    return q / np.sum(q, axis=-1, keepdims=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the M-step, we take the derivatives of $\\mathcal{L}(\\boldsymbol{\\theta}, q)$ w.r.t. to $\\pi_c$, $\\boldsymbol{\\mu}_{c}$ and $\\boldsymbol{\\Sigma}_{c}$ and set the resulting expressions to $0$ i.e. do MLE of parameters and also apply constraints to ensure that $\\sum_{c=1}^C \\pi_c = 1$ and $\\boldsymbol{\\Sigma}_{c})^T$ is positive semi-definite. The details are omitted here and only the results are presented.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\pi_c &= {1 \\over N} \\sum_{i=1}^N q(t_{ic} = 1) \\tag{16} \\\\\n",
    "\\boldsymbol{\\mu}_{c} &= {{\\sum_{i=1}^N q(t_{ic} = 1) \\mathbf{x}_i} \\over {\\sum_{i=1}^N q(t_{ic} = 1)}} \\tag{17} \\\\\n",
    "\\boldsymbol{\\Sigma}_{c} &= {{\\sum_{i=1}^N q(t_{ic} = 1) (\\mathbf{x}_i - \\boldsymbol{\\mu}_{c}) (\\mathbf{x}_i - \\boldsymbol{\\mu}_{c})^T} \\over {\\sum_{i=1}^N q(t_{ic} = 1)}} \\tag{18}\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m_step(X, q):\n",
    "    \"\"\"\n",
    "    Computes parameters from data and posterior probabilities.\n",
    "\n",
    "    Args:\n",
    "        X: data (N, D).\n",
    "        q: posterior probabilities (N, C).\n",
    "\n",
    "    Returns:\n",
    "        tuple of\n",
    "        - prior probabilities (C,).\n",
    "        - mixture component means (C, D).\n",
    "        - mixture component covariances (C, D, D).\n",
    "    \"\"\"    \n",
    "    \n",
    "    N, D = X.shape\n",
    "    C = q.shape[1]    \n",
    "    sigma = np.zeros((C, D, D))\n",
    "    \n",
    "    # Equation (16)\n",
    "    pi = np.sum(q, axis=0) / N\n",
    "\n",
    "    # Equation (17)\n",
    "    mu = q.T.dot(X) / np.sum(q.T, axis=1, keepdims=True)\n",
    "    \n",
    "    # Equation (18)\n",
    "    for c in range(C):\n",
    "        delta = (X - mu[c])\n",
    "        sigma[c] = (q[:, [c]] * delta).T.dot(delta) / np.sum(q[:, c])\n",
    "        \n",
    "    return pi, mu, sigma    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For computing the lower bound, using the results from the E-step and M-step, we first re-arrange Eq. $(11)$ \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mathcal{L}(\\boldsymbol{\\theta}, q) &= \n",
    "\\sum_{i=1}^{N} \\mathbb{E}_{q(\\mathbf{t}_i)} \\log {{p(\\mathbf{x}_i, \\mathbf{t}_i \\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i)}} \\\\ &=\n",
    "\\sum_{i=1}^{N} \\sum_{c=1}^{C} q(t_{ic} = 1) \\log {{p(\\mathbf{x}_i, t_{ic} = 1 \\lvert \\boldsymbol{\\theta})} \\over {q(t_{ic} = 1)}} \\\\ &=\n",
    "\\sum_{i=1}^{N} \\sum_{c=1}^{C} q(t_{ic} = 1) \\left\\{ \\log p(\\mathbf{x}_i \\lvert t_{ic} = 1, \\boldsymbol{\\theta}) + \\log p(t_{ic} = 1 \\lvert \\boldsymbol{\\theta}) - \\log q(t_{ic} = 1) \\right\\}\n",
    " \\tag{19}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "and then implement it in this form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lower_bound(X, pi, mu, sigma, q):\n",
    "    \"\"\"\n",
    "    Computes lower bound from data, parameters and posterior probabilities.\n",
    "\n",
    "    Args:\n",
    "        X: observed data (N, D).\n",
    "        pi: prior probabilities (C,).\n",
    "        mu: mixture component means (C, D).\n",
    "        sigma: mixture component covariances (C, D, D).\n",
    "        q: posterior probabilities (N, C).\n",
    "\n",
    "    Returns:\n",
    "        Lower bound.\n",
    "    \"\"\"    \n",
    "\n",
    "    N, C = q.shape\n",
    "    ll = np.zeros((N, C))\n",
    "    \n",
    "    # Equation (19)\n",
    "    for c in range(C):\n",
    "        ll[:,c] = mvn(mu[c], sigma[c]).logpdf(X)\n",
    "    return np.sum(q * (ll + np.log(pi) - np.log(np.maximum(q, 1e-8))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model training iterates over E- and M-steps alternately until convergence of the lower bound. To increase the chance of escaping local maxima and finding the global maximum, training is restarted several times from random initial parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower bound = -3923.77\n"
     ]
    }
   ],
   "source": [
    "def random_init_params(X, C):\n",
    "    D = X.shape[1]\n",
    "    pi = np.ones(C) / C\n",
    "    mu = mvn(mean=np.mean(X, axis=0), cov=[np.var(X[:, 0]), \n",
    "                                           np.var(X[:, 1])]).rvs(C).reshape(C, D)\n",
    "    sigma = np.tile(np.eye(2), (C, 1, 1))\n",
    "    return pi, mu, sigma\n",
    "\n",
    "\n",
    "def train(X, C, n_restarts=10, max_iter=50, rtol=1e-3):\n",
    "    q_best = None\n",
    "    pi_best = None\n",
    "    mu_best = None\n",
    "    sigma_best = None\n",
    "    lb_best = -np.inf\n",
    "\n",
    "    for _ in range(n_restarts):\n",
    "        pi, mu, sigma = random_init_params(X, C)\n",
    "        prev_lb = None\n",
    "\n",
    "        try:\n",
    "            for _ in range(max_iter):\n",
    "                q = e_step(X, pi, mu, sigma)\n",
    "                pi, mu, sigma = m_step(X, q)\n",
    "                lb = lower_bound(X, pi, mu, sigma, q)\n",
    "\n",
    "                if lb > lb_best:\n",
    "                    q_best = q\n",
    "                    pi_best = pi\n",
    "                    mu_best = mu\n",
    "                    sigma_best = sigma\n",
    "                    lb_best = lb\n",
    "\n",
    "                if prev_lb and np.abs((lb - prev_lb) / prev_lb) < rtol:\n",
    "                    break\n",
    "\n",
    "                prev_lb = lb\n",
    "        except np.linalg.LinAlgError:\n",
    "            # Singularity. One of the components collapsed\n",
    "            # onto a specific data point. Start again ...\n",
    "            pass\n",
    "\n",
    "    return pi_best, mu_best, sigma_best, q_best, lb_best\n",
    "\n",
    "pi_best, mu_best, sigma_best, q_best, lb_best = train(X, C=3)\n",
    "print(f'Lower bound = {lb_best:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After convergence we can use the posterior probabilties of latent variables to plot the soft-assignment of data points to mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(X, color=q_best)\n",
    "plot_densities(X, mu=mu_best, sigma=sigma_best)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal number of components\n",
    "\n",
    "Usually, we do not know the optimal number of mixture components a priori. But we can get a hint when plotting the lower bound vs. the number of mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Cs = range(1, 8)\n",
    "lbs = []\n",
    "\n",
    "for C in Cs:\n",
    "    lb = train(X, C)[-1]\n",
    "    lbs.append(lb)\n",
    "    \n",
    "plt.plot(Cs, lbs)\n",
    "plt.xlabel('Number of mixture components')\n",
    "plt.ylabel('Lower bound');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a strong increase in the lower bound value until $C = 3$ and then the lower bound more or less doesn't increase any more. With more components there are of course more options to overfit but the simplest model that reaches a relatively high lower bound value is a GMM with 3 components. This is exactly the number of components used to generate the data.\n",
    "\n",
    "A more principled approach to determine the optimal number of components requires a Bayesian treatment of model parameters. In this case the lower bound would also take into account model complexity and we would see decreasing lower bound values for $C \\gt 3$ and a maximum at $C = 3$. For details see section 10.2.4 in \\[1\\].\n",
    "\n",
    "### Implementation with scikit-learn\n",
    "\n",
    "The low-level implementation above was just for illustration purposes. Scikit-learn already comes with a `GaussianMixture` class that can be readily used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "gmm = GaussianMixture(n_components=3, n_init=10)\n",
    "gmm.fit(X)\n",
    "\n",
    "plot_data(X, color=gmm.predict_proba(X))\n",
    "plot_densities(X, mu=gmm.means_, sigma=gmm.covariances_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are very similar. The differences come from different random initializations. Also, plotting the lower bound vs. the number of mixture components reproduces our previous findings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Cs = range(1, 8)\n",
    "lbs = []\n",
    "\n",
    "for C in Cs:\n",
    "    gmm = GaussianMixture(n_components=C, n_init=10)\n",
    "    gmm.fit(X)\n",
    "    lbs.append(gmm.lower_bound_)\n",
    "    \n",
    "plt.plot(Cs, lbs)\n",
    "plt.xlabel('Number of mixture components')\n",
    "plt.ylabel('Lower bound (normalized)');"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The lower bound values obtained via `gmm.lower_bound_` are normalized i.e. divided by $N = 1000$ in this example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Inference of latent variables and estimation of parameters in GMMs is an example of exact inference. The exact posterior can be obtained in the E-step and analytical solutions exist for parameter MLE in the M-step. But for many models of practical interest, exact inference is not possible and approximate inference methods must be used. *Variational inference* is one of them and will be covered in [part 2](latent_variable_models_part_2.ipynb), together with a *variational autoencoder* as application example. \n",
    "\n",
    "## References\n",
    "\n",
    "\\[1\\] Christopher M. Bishop. [Pattern Recognition and Machine Learning](http://www.springer.com/de/book/9780387310732) ([PDF](https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf)), Chapter 9.  \n",
    "\\[2\\] Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapter 11.  \n"
   ]
  },
  {
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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